In a chafing dish or skillet, melt the butter over medium heat.
Add the flour, salt, and pepper, and stir to combine, cooking for 1-2 minutes until the mixture is bubbling and golden.
Gradually pour in the milk, stirring constantly to prevent lumps from forming.
Add the chopped egg whites to the sauce, stirring until heated through.
Toast the bread slices until golden brown.
Place the toast slices on serving plates and spoon the creamy egg mixture over the toast.
Using a fine strainer, rub the egg yolks over the top of each serving.
Garnish with chopped parsley.
Serve the Creamy Eggs on Toast immediately.